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This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Multi-step planning has been widely employed to enhance the performance of large language models (LLMs) on downstream natural language processing (NLP) tasks, which decomposes the original task into multiple subtasks and guide LLMs to solve…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Non-stationary domains, where unforeseen changes happen, present a challenge for agents to find an optimal policy for a sequential decision making problem. This work investigates a solution to this problem that combines Markov Decision…
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…
Large vision transformers present impressive scalability, as their performance can be well improved with increased model capacity. Nevertheless, their cumbersome parameters results in exorbitant computational and memory demands. By…
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…
ACLP is a system which combines abductive reasoning and constraint solving by integrating the frameworks of Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). It forms a general high-level knowledge representation…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
We study the set of optimal solutions of the dual linear programming formulation of the linear assignment problem (LAP) to propose a method for computing a solution from the relative interior of this set. Assuming that an arbitrary…
Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…
Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
We study the Maximum Budgeted Allocation problem, which is the problem of assigning indivisible items to players with budget constraints. In its most general form, an instance of the MBA problem might include many different prices for the…
We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert…
In this paper we provide faster algorithms for approximately solving discounted Markov Decision Processes in multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with $|S|$ states, $|A|$ actions, discount factor…